This paper proposed a distributed parallel decomposition algorithm for solving linearly coupled block-structured nonconvex constrained optimization problems.
Such structures naturally arise in several applications, including nonlinear model predictive control and stochastic optimization.
The algorithm performs Jacobi updates of the augmented Lagrangian function with appropriately chosen proximal terms, requiring only local solutions of the individual block NLP problems.
By constructing an easily computable Lyapunov function, we showed that the algorithm converges globally to \(\epsilon \) -approximate stationary points in \(O(\epsilon ^{-4})\)  iterations as well as locally to \(\epsilon \) -approximate local minimizers of the original NLP at a sublinear rate.
We also provided a simple, practical and theoretically convergent variant of the algorithm where its parameters are adaptively tuned during the iterations.
Our numerical experiments show that it can outperform existing algorithms based on ADMM and that optimizing large-scale nonconvex AC optimal power flow problems over more than 100 time steps can be done in the order of roughly one hour.
Future work includes the study of acceleration techniques such as inexact NLP solutions and momentum methods, integration with the two-level algorithm of [1]}, as well as the incorporation of second-order information such as in [2]}.
